Thomas M. CoverIn Memoriam1938-2012

Tom Cover, one of the greatest information theorists and a wonderfully inspiring teacher and mentor, died in Palo Alto on March 26, 2012. During his 48 year career as a professor of Electrical Engineering and Statistics at Stanford University, he graduated 63 PhD students, authored over 120 journal papers in learning, information theory, statistical complexity, and portfolio theory; and he coauthored Elements of Information Theory, the most widely-cited book in the field. In recognition of his seminal contributions, Tom Cover received many awards and honors, including the IEEE Information Theory Society Claude E. Shannon Award, the IEEE Richard W. Hamming Medal, and the Outstanding Paper Award in information theory. He was a Fellow of the IEEE and a member of the National Academy of Engineering and the American Academy of Arts and Sciences.

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Tom was my doctoral thesis advisor and taught me how to do research, not by what he said, but by what he did. I was truly blessed to have him as an advisor, friend and colleague. He will be sorely missed.

I remember the first time I was in a committee with Tom as chair. After some chatting and jokes etc I started to be a bit impatient. So I asked: `Tom, how should we proceed?’ and the answer was `Let’s do something inefficient for a while’

Just a few weeks ago, after Tom’s “Super St Petersburg Paradox” talk, we had a very happy chat on the topic in his office, towards the end of which he said “come join our group meeting every wednesday afternoon”. I said “then I will take some more of your wisdom”, and he said “oh, it is very cheap”. Just can’t believe we lose him in such a sudden. His wisdom and generosity will live on.

I met Tom for the first time some 20 years ago. He had a corner office in the Durand building where he used to spend long evenings. Tom was a renaissance person with whom you could discuss everything under the sun and the stars. The news of his passing away comes as a terrible shock to many. My most sincere condolences to his family.

Tom was truly a unique individual. What I loved the most about him was his honesty, straightforwardness and clearness of mind, in addition to his unusual creativity and brightness. He was truly a scientist in the right meaning of it.

For me, Tom was, first of all, one of the best symbols and advocators of the beauty and elegance of Information Theory. We never collaborated, but I was lucky to have many inspiring conversations with him, in conferences, and during my summer visits to HP Palo Alto, when he used to invite me to Stanford. He is one of my role models, both professionally and otherwise. He will be truly missed.

Tom was always an inspiration and a wonderfully joyful spirit to have around in ISL. Just weeks ago, I met him in the corridor, and he told me a rib-tickling joke about the ‘most interesting man in the world’ (from the Dos Equis ad campaign). Here it is:
“The most interesting man in the world once had an awkward moment……….
just to see what it felt like.” Hilarious as usual.

And then Tom signed off with, “Let me know when you’ll be defending your thesis.”

I feel very fortunate to have had Tom as an advisor for 3 years. He always has creative ideas, a great sense of humor and the ability to make learning fun and easy. He puts his students ahead of himself at all times. His research seminars break all barriers to creativity. Five years ago, he made a brave choice to forgo his liver surgery so he could teach at Stanford for the rest of his life. He is an irreplaceable loss. As his student, I make it my responsibility to carry his vision forward.

Tom was a kind man as well as a fantastic information theorist, able to simplify complex concepts so most could understand. He’d check on me periodically through my career at Stanford usually with sound advice. I remember my dog, Shannon, loved to go sit in Tom’s office, and he thought it fate/funny because of the name (never complained). May god rest Tom in asymptotic equality and happiness.

I was shocked and saddened by Tom’s passing away. I remember very vividly my first class in Information Theory, 43 years ago. He made me discover the beauty and the elegance of the field.
He was an inspiring mentor, driving everybody who worked with him to achievement. Even though we have not been much in touch in recent years, the thought of his departure leaves a painful giant hole in my memory.

I can’t find the words to describe how sad I am that we lost Tom. I will always remember him not only as the giant figure he was in our community but also as the enthusiastic, sincere, delightful person he was I loved being around. During the time I served our community at the NSF, he generously supported the theory program with his time and energy despite his health problem. Random memories of him are rushing through my head; like his encouraging yet tough reviews, his winning proposal that was the most concise one I ever saw, his gentle amusement on one of our fast paced panels as he teased me for being a “slave driver,” his warm smile, the love in his eyes and in his voice as he talked of his family…

“We all know the feeling that follows when one investigates a problem, goes through a large amount of algebra, and finally investigates the answer to find that the entire problem is illuminated not by the analysis but by the inspection of the answer.”

At the start of one group meeting, Tom announced that a new game show was coming in a few months, one that he found very exciting. Several people would be stranded on a desert island, put through various challenges, and every week the group would vote to expel one of its members. While I was horrified at the premise and potential for things to go awry in this brave new experiment in television, Tom was already thinking ahead to the various strategies contestants would employ, this being a unique laboratory for applied game theory. (Here I’m borrowing the term some members of our group would later use to refer to the informal poker tournaments that occasionally punctuated our research days.) While this was not the most esteemed use of Tom’s energy, it might have been one of the most representative: He always thought about the application of math and science to the world, whether it be in sport, in finance, in telecommunications, or even in Survivor.

Or, this week, to the lottery. Tom consulted for the California lottery and I remember him saying how, since every ticket had an equal probability of winning, a player’s goal should be to lower the chance that others would win too. For example, since many people pick dates as “lucky numbers,” the numbers 1 through 31 were overrepresented on tickets, and one strategy would be to play numbers only over 31. With yesterday’s record-breaking jackpot, I decided to put this to the test and buy my first lottery ticket since he told me this. Only one of my numbers was correct, 38, which I’d chosen in honor of Tom’s birth year. I will miss him, but he’s certainly provided those who’ve known him with numerous memories, and the rest of the world with numerous scientific contributions.

By the way, a few years ago I set up Google Groups b-coverians (for those in the Bay Area) and c-coverians (for those who go to conferences) in order to get us Coverians together when the opportunity arises, e.g., a lunch at ISIT or a dinner in Palo Alto. We’ve met a few times over the years, and I hope we continue this tradition.

Tom,
I am writing to you directly as it’s hard to believe you are gone. You were always a great inspiration for me, even though I didn’t have the opportunity to be one of your many students (whom I envy a lot!).
I always thought of your book as the perfect balance between rigor and fun. The book shows the large variety of topics you were interested in: physics, games, horse races, gambling, sports, statistics, information theory.. (and also your fresh approach to research and life in general!) Lastly, you always gave me the impression that you saw us all as equal: young and old, junior and senior.

Come to think of it, those poker games were “applied probability theory,” and they’d replaced football breaks, some of which saw a 60-some-year-old Tom playing QB. Whether for his height, his wit, or his wisdom, he was always in demand. I recall an ISIT talk that swelled to double capacity and nearly double time, too, quite befitting Tom’s loose notion of time; if he could give ten of us “two minutes” which lasted 90 or 100 minutes total, he was certainly due a little extra time himself.

My first enocounter with Information Theory came up when I accidentally found Tom’s Stanford University technical report on gambling and its relation to data compression. This work motivated and influenced deeply much of my work along my career. I then met Tom and our discussions were always inspiring. When he gave me a preliminary version of his book I felt blessed, and immediately used it for teaching and for reference. Tom represents Information Theory; his work and his personality show why it is such an intriguing and inspiring field. I remember what he said, that in Theorems, like in good jokes, you must look for the “punch line”. And like a good joke, research should be fun. I will miss our discussions and will I miss him – his humor and wit, and his wisdom.

Tom was my assigned advisor when I arrived at Stanford, and ended up as my 2nd advisor. When I popped my head into his office in Sept 1990 to introduce myself, he responded from a cloud of smoke, announcing that today he had concluded that “there is no underlying reality!” Thereforth launched some kind of thought experiment in which we concluded that 2/3 = 1/2. Every time I went to speak with him, we went through some type of activity like this first. I have so many memories of him that make me smile.

Professor Tom Cover was my MS program advisor. I still remember the first time when I went to his office and ask for advise on choosing courses. At first, I never expect a MS program advisor to be so kind and patient. But when I went to talk to him, he asked a lot about my interest and proper courses for me. After that, he also talked about what he thought the future of technology would be. This inspires me a lot and gave me a lot of encourage to begin my study in Stanford, especially at the time I just arrive in here. I never stop thinking what a wonderful person he was and how lucky I am to have him as my advisor. Even though I don’t have as much memory as others since I only met him twice in the two quarters I’ve been here, his great personality and attitude to technology still impressed me a lot. I am so sad and shocked when I heard the bad news. I still couldn’t believe he won’t continue to give me advice on courses and approve for my proposal in final quarter. It is a great loss for everyone. He will be remember by me and by all the people who love him and he loved.

Besides being a great information theorist, a shrewd poker player, and a good friend, Tom was a pretty darn good golfer. I hope he finds a nice place to “tee it up” in the great beyond. I believe Tom had attended every ISIT since 1966 in Los Angeles, a record stretch. ISIT 2012 in Boston won’t be the same without him. We will miss him.

This is sad and shocking news. I had no idea that Tom was so sick. He was a lovely friend and colleague, with a powerful, supple and playful mind. His talks were invariably beautiful. He will be very much missed.

It is hard to imagine that Tom Cover is no longer with us. He was my guru, my teacher, my mentor and my friend. Words cannot express how much I owe him. Over the many hours spent at his office, we talked not only about Information Theory, but about gambling, sports, the stock market and physics. The breadth of his interests and his keen insight that simplified even the most complex problems were always an inspiration. His wisdom and unique genius will forever be missed.

Being something of an information theory outsider, my connection to Tom was primarily through personal e-correspondence over the years. However, even at such a remove, it was immediately clear that he was the epitome of the gentleman-scholar.

I don’t know of many (if any) other information theorists who so naturally occupied the world stage and did so with such humor and humility. Through his broad ranging intellect, he helped the world see that information theory was not only for digital communication but for just about everything — including that most fundamental of human “sciences” economics. In fact, Tom’s work on portfolio theory drew a hilariously direct (if ultimately misdirected ) broadside from one of the lions of economic theory, Paul Samuelson (Nobel Prize in Economic Sciences, 1970). Tom e-laughingly shared a “words of one syllable” lampoon** with me long ago as a “shot in the arm” to remind me that new ideas are often not accepted (if not attacked) initially.

Almost needless to say, Tom’s work stood the test of time.

So it’s easy to see that what shone through about Tom was his gentleness, humanity and wit — no acerbic intellectual was he. Certainly the field will miss him, but I think that the loss goes far beyond the usual when it comes to Tom. I am certain that for many many people, even those like me who spoke with him in person only very seldom, it feels like we’ve also lost one of our best friends.

I was fortunate to have been one of Tom’s PhD students and to have collaborated with him on some papers. Thinking of Tom brings back fond memories of working with him in his office, the group meetings, the gatherings at his home with Karen, his wonderful lectures and talks. One particularly indelible memory of Tom is hearing from him about a harrowing incident involving a teenager crashing a car through Tom and Karen’s bedroom wall, and how, after things settled down, incredibly, Tom wound up giving the kid a ride home. Another is of a group meeting round robin when Jim Roche posed the problem of finding the probability that N points selected randomly on a circle can all be covered by a semi-circle. After looking around for a moment to see if anyone would be chiming in, Tom stood up and said that, by chance, he happened to be one of the world’s foremost experts on this problem and proceeded to give a clear-as-a-bell impromptu lecture on the solution to the general n-dimensional sphere/hemisphere version of the problem using an ingenious conditioning argument. It was a virtuoso performance I will never forget. It would take many more words to describe the impact Tom’s intellect, generosity of spirit, and all around “coolness”, have had on my life and career. I will always be grateful to him.

Like many, I am deeply saddened by his passing. I met Tom when I showed up at Stanford in 1972 and asked, “so tell me, Tom, what do I need to do to earn a Ph.D.?” He told me, and thus began our forty-year friendship. His quick wit and deep thoughtfulness remained an inspiration each time I saw him over the years.

Within a single year we have lost both Jack Wolf and Tom Cover, two of my favorite people as well as two of the most brilliant and entertaining information theorists. Both had an ability to distill and unravel a complicated problem into a clear an elegant solvable core. Tom was much closer to home, however, and the world is diminished without him in it. I knew him best during the 70s and 80s, when we saw each other at conferences and workshops almost as often as we did at Stanford. Perhaps my favorite memory is when I had the best meal of my life when Tom encouraged Lolly and me to join him at a two star Paris restaurant in June 1973, after the Ashkelon ISIT, where the first Shannon lecture was given by Shannon himself. The meal cost a fortune by our junior faculty standards; I still remember the pile of francs, dollars, and travelers’ checks piled up in the middle of the table. Tom bought the wine and sparked the conversation and the evening was well worth every centime.

I am deeply saddened to hear that Professor Cover is no longer with us. Not only did I have the chance to have him as a teacher, I also was fortunate enough to have many stimulating conversations with him on a range of subjects. Even though I was not one of his doctoral students, he always took the time to talk to me about almost anything and he always had good advice. We did not only lose a great scholar, we also lost a great person. Stanford will not be the same without him.

The first dinner I had with Tom was in May 1999. I was an undergrad junior who just discovered Tom’s courses on information theory two quarters ago, and started having regular chat with him during his smoking break outside the corner office in Durand Building, the most intellectually exciting journeys into uncharted and unexpected territories: sports, gambling, poker, what is duality, is information mathematical or physical… When my dorm gave each of us an opportunity to invite a faculty who influenced us most to a dinner, I was so excited Tom accepted the invite and shared his time so generously, as he always did to even the undergrads. He told me later that he would be my “umbrella advisor”: I could always work with him but also would be free to explore any other subjects with other faculty. Tom is as generous as he is brilliant.

I remember the dinners I missed while going through rounds after arounds of editing a paper with Tom, or more accurately, of Tom rewriting the entire draft line by line by hand, in his Coverian large font on pads of yellow college-ruled paper. Every word, every arrow in each graph, every subscript in each notation were edited and re-edited. I was so hungry and quickly got impatient. But Tom never compromised a single bit on the quality of his scholarship and his writing.

I also remember the last dinner I had with Tom, in October 2010 at Palo Alto’s Three Seasons. Tom suggested the restaurant, and told jokes about “shaking beef” on the menu. He enjoyed telling jokes, and making fun of his own research. He once said good research results should be like good jokes, crisp and surprising, you couldn’t see it coming and then it became obvious once you saw it. Tom showed me that vigorous thinking is so much fun, and you can always laugh when you’re “doing research.”

Tom waved me goodbye, as the autumnal sunset dimmed above Three Seasons’s patio. Never crossed my mind that there would not be another chance to see him, to talk to him, to miss or to have another dinner with him. I thought it would be just like back in the spring of 1999, when I eagerly explained every turn from Wilbur Hall to Durand so that Tom wouldn’t have to waste even more time after spending a whole evening chatting with an undergrad. Back then, Tom smiled: “You bet” and off he went. Then I met with him the next day, more chats that tickled imagination… I thought I’d see him again soon. I knew I would. But now I’m wrong. And in so many people’s hearts, the world is dimmer without Tom.

I fondly remember the many interactions I had with Prof. Cover in and around Packard.
You could freely walk into his office and talk about many interesting subjects. I enjoyed talking to him about martingales. Though it was not his area of research, he attended a few talks I gave in the dept. during my PhD and even had related questions to ask afterwards. He was such an inspiring person to talk to. Learning the news of him passing away felt very sad. May he rest in peace. I feel privileged to have known him.

Over almost half-a-century, I have met hardly any individual of the stature of Tom. Not only as a scientist. He was of course a giant. But also as a human being. His humor, his personality, his honesty, his good disposition, his caring nature, his love of quality in everything. I have too many fond memories of Tom to share here. I will always remember him as what is best in the Society of Indoemation Theory.
Tom, you have not left us. You are still with us. In our minds, in our souls, in our lives.

Tom was my colleague in the stat department for twenty years. What I will never forget is the beauty and purity of his interests. Three of his specific interests exemplify this for me. First, his interest in in counting the number of regions of Euclidean space carved out by a random system of linear inequalities. Second his interest in kolmogorov complexity. Third, his interest in analogies between entropy power inequalities and brunn minkowski. All of these turned out to have real importance in my life, and I’m grateful to have had guidance from Tom either in writing or in person about the significance of these fundamental topics. When he wrote in his Shannon lectures that information theory has a kind of beauty and completeness comparable to physics he represented a very important viewpoint, but one so seldom voiced confidently and explicitly. Thanks Tom, it has been a privilege.

Tom’s lectures were always an inspiration; words of almost poetic simplicity explaining the most abstract and profound concepts, and a cadence that conveyed a sense of wonderment, as if he was just discovering the incredible elegance of his chosen subject.

Tom was a wonderful colleague during the twelve years I have been at Stanford, and his personal warmth, charisma, and wisdom will be missed greatly.

During my ten plus years as Tom’s colleague it was impossible to overlook his brilliance, but probably even harder to miss his great dry humor and the stellar impact he had on my students and others. I will sorely miss Tom, and my sincere condolences are with his family and friends.

I still have a hard time believing that Tom has passed away. Only a few weeks ago we were having great conversation over lunch at ITA in San Diego.
Studying with Tom was one of the greatest privileges of my life. (I was his #28, out of 64 PhD students he led to graduation. Interesting how the powers of two are attracted to the man.) He taught me many things and has been a role model for me in many ways. No matter how difficult the situation was, Tom always had a clever way to save the day. I treasure some wonderful memories of the last 35 years.
When we die, our memories live in R^n. Tom´s memories live in a space with a large number of dimensions. Generosity, brightness, congeniality, creativity, friendliness, fast thinking, wisdom are just a few. Tom had the unusual ability to see things well in R^n. I remember him explaining in lectures how dark the space was. That is because light goes down with the distance raised to power (n-1). You can’t see the tip of your nose, he used to say. Now the memories of our beloved Tom are sure to bring some extra light to this place.

I only knew Tom for around one year. However, that time was more than enough to appreciate his charismatic personality. It was last February that I decided to talk to him and meet him in person. He welcomed me in his office as if we were good old friends! After that, I started going to the Wednesday meetings and in June he honored me when he decided to become my advisor. Throughout all our discussions this year, Tom’s precision, clarity, kindness, humbleness and generosity were more than impressive.
I recently asked Tom: “Would you like to play poker with us (some students from the lab)?” He eagerly answered: “Of course!” We would ask him to arrange a specific time and place in the following Wednesday meeting. That meeting never came.

Thank you Tom for your trust. It has been an honor. My deepest condolences to his family.

It’s hard to imagine that someone who you enjoy so much is no longer around. He’s the best friend, the father or brother, who you look forward to seeing whenever occasion permits. Approachable and comfortable, but always on top of his game. His witty humor and inquiries often encourage you to pause, step back from your pursuits, and look for a broader perspective.

I met Tom during my first year of graduate school by taking his class (knowing nothing about information theory except that Steven Boyd had recommended the class to me). A year later I accepted his warm invitation to join his research group when it became overwhelmingly obvious to me how much I would enjoy the experience. I could never have anticipated how much my life would be influenced by my experience in graduate school. Thanks Tom, for your invaluable friendship and guidance.

I never knew him but I admired him for the quality of his work. His book is like a “bible” in the field of Information Theory. It is very sad when great personalities leave this world. My condolences to his family.

In the Ph.D. quals of 1968, Tom Cover was one of my 10 examiners. Knowing little about information theory, I didn’t know what to expect. I was stunned when he asked how gravity would work in a 2-D universe. I rambled for the requisite 10 minutes, but actually look back somewhat fondly on that experience. I didn’t become an information theorist, but I sensed the subject was in good hands as we distantly crossed paths over the next 40+ years. Last evening I opened the April 2012 Scientific American and discovered the only article on 2-D gravity I’ve ever seen, published within a few days of his death.

Tom,
I learned Information Theory from your book, as did so many thousands of other students. It has been such an honor to be your colleague in the Center for Science of Information. You’ve touched the lives of so many people, and you continue to live in our hearts, and in our work. You’re an inspiration to us all.

Tom was absolutely one of my best professors at Stanford. His enthusiasm for teaching and learning was contagious. He always had time for questions and was interested in what was going on in my life. His sense of humor was priceless. Tom will be greatly missed by all of us who experienced the joy of counting him as a friend and mentor.

I first met Tom when I came to Stanford in 1991. To the green wide-eyed student coming from abroad that I was, Tom was the embodiment of all the characteristics I had imagined a true scholar would have: great depth, wit, generosity and a hint of mystery that always lurks beneath the surface.

After all these years, I have encountered few who match Tom in the above.

Tom was always incredibly kind and generous with his time. A current student of mine who met Tom for the first time at the 2012 ITA was marveling at how much time the “great Tom Cover” had spent chatting with him and how genuinely interested in his work he had been.

What a huge loss. But what a great fortune for those of us who still have the many memories, can read his book and articles, and can see his research style living on in the numerous students he has influenced.

I graduated from Cornell in 1988 and was applying for a teaching job. In the template of my application letter, there was the sentence “I would be very happy to come to Berkeley for an interview.” The whole thing turned into a nightmare for me when I discovered that I had forgotten to substitute the word “Berkeley” in my applications to all other universities. I then immediately sent out apology letters for my stupidity, though in my mind the damage had already been done.

A few weeks later, I received a letter from Tom. I almost could not believe that Tom, a giant in the field whom I had never met before, would write me a two-page reply letter. He started by comforting me, saying that “Berkeley and Stanford are worthy substitute of each other.” Then he went on to say that since at Stanford they already had Marty Hellman, Bob Gray, Abbas El Gamal, and himself, they were not hiring in the information theory area. In order not to completely disappoint me, he added that “Your employment at Stanford would be possible somewhere down the road after you have established your individual reputation.”

I never had the privilege of being a colleague of Tom, but I really thank him not only for his kindness of lifting me from the nightmare, but also for his great support early in my career.

I subsequently heard of similar kindness of Tom from many different people, so my experience was not a unique one. Tom will be greatly missed and fondly remembered by all of us.

Wow. What a surprising and deep loss.
Tom appropriately exerts a huge influence not only on his students but also on whole fields of investigation.

The bridging of information theory and statistics is a key example. Let me tell the story how he exerted this influence on me, starting with arrival for graduate work at Stanford at the Information Systems Laboratory in 1981 having had an undergrad background at Rice and summer jobs at a company that did empirical modeling using polynomial neural nets (a topic for which Tom had foundational capacity results in his early academic years in the 1960s). The most captivating course that first fall was the information theory course. When Tom drew the information balls in the simplex that show the geometry of the distribution of empirical measures and when he discussed the role of universal data compression in capturing what is of essence to be learned from data, I was captivated and came to him wanting to learn more. Together we wanted to have a criterion for model selection with general motivation and analysis without being locked into a particular sequence of model choices, and the compression story provides the right framework.

Tom dramatically shaped my path in three ways. First he explained that with such interests one should go take as many probability and statistics classes as possible from the stat department, plus his classes in advanced information theory, pattern recognition, and info&stat, along with other relevant ISL fare.

Secondly, in weekly individual and group meetings over the next four years, Tom exemplified that the best research occurs when there is a simple surprise in the understanding of what might be thought of as a deep result. After all there are not too many simple things to go around (Tom’s favorite Kolmogorov theory quantifies this).
So if something is new, important, and simply explained it is rare indeed!

Thirdly, Tom was a point of attraction for interesting people at Stanford. The list is huge, but for me I call attention to my office mates Max Costa, David Larson, David Glus, plus Paul Algoet next door, and later students like Hal Stern, Andrew Nobel and Ioannis Kontoyiannis who continued the stat&info connection (some of whom were part of the Cover group meetings but had other advisors from stat). Earlier and continuing connections were established between Tom and familiar statisticians like Brad Efron and Harvard’s Carl Morris and information theorists like Abbas El Gamal and Bob Gray. Plus there was an interesting stream of visitors, including, for instance, Rudy Alswede and Imre Csiszar, who shared our office and daily info&stat conversations for at least a term.

We shall honor Tom the best if continue to champion information theory as the banner that holds together the quantitative disciplines within engineering, statistics, mathematics, and the sciences. This is his legacy.

I met Tom last year when I came to Stanford, and I had the pleasure of attending his meetings every wednesday. He was a very nice person and passionate about what he was teaching. I will miss him and his puzzles.

Tom was at the top of my list for the quals, and the only one of my top 10 that I didn’t get, but instead I got to spend the next 5 years studying with him. He told me about an 8am seminar class at MIT; he once woke up in the midst of a different seminar than the one he fell asleep in. Every day with Tom had electricity and excitement. He would compose equations (inequalities, usually) with a Magic Marker on small yellow pads…sometimes the most startling and beautiful derivations. But in addition he was a wonderful friend and mentor. I was lucky to know him so well but that much sadder that he’s gone.

I was a PhD student with Tom in the 80′s, and one of the funny memories I have of Tom was that he named his dog “zero”, since that would make it simple to sequentially name all subsequent dogs. I didn’t recognize it at the time, but Tom was to become the gold standard of teacher/supervisor for me. While he never compromised standards, he also always made it clear that work and life were only worth the effort if they were both joyful and rewarding. He will be missed, and will also live on in the memories and behaviors of the people he touched.

Tom was unique in his ability to explain complex ideas in the simplest way. His papers and textbook display how really simple some complex-looking ideas are. He made information theory and related fields accessible to a large crowd.

I have fond memories of our research group meetings in his corner Durand office with Abbas ElGamal, Roger King, Jan Van Campenhout, Kieth Jarret, Chris Heegard and Max Costa. His wit, wisdom, and vision made our meetings vibrant and productive.

Tom was a brilliant thinker, a productive researcher, a great mentor, and a true friend. I was lucky having him as my advisor. He will be greatly missed!

Tom had many things to teach, and many of us learned a great deal from him. For me, his most important lesson never appeared in a lecture, or a book, or a paper, but ran as a common thread through all these. The lesson was Tom’s (impeccable) research aesthetics. He asked questions that were surprising, fundamental, and illuminating. His answers were elegant and simple. On paper Tom wrote with a dull pencil, on the blackboard with oversize chalk. He never let details get in the way of the big picture.

Tom’s passing is a loss, professional and personal, for all of us. He will be missed.

Tom will be greatly missed. His integrity, generosity and intellect were an asset to his colleagues and to the larger IT community. His wry sense of humor was a delight at many a faculty meeting. His humility and simplicity was an example to all of us.

In 1992, I did talk to him about my ideas on MIMO spatial multiplexing – he was curious and an early believer, but to my regret, I did not manage to get him interested enough to work on MIMO information theory!

We all know death is inevitable; nevertheless when it occurs to someone as tremendous as Tom, it is really hard to fathom and leaves me in great agony. Information Theory has lost one of its foremost pioneers. Beyond a great mentor and teacher, Tom for me was the personification of the ultimate EE professor and researcher. His communication was impeccable both in person as well as in theory. His personality was dynamic, very approachable and pleasant. His courses and teaching style were engaging and entertaining. I have never seen anybody present such complex subject matter in such a simple and elegant fashion. We will not witness anybody like him again. It was a privilege to get my doctorate under his awesome guidance. I will sorely miss his enthralling presence.

Tom and I met in the Fall of 1960 as
new Stanford grad students. In the next
52 years I never heard him say anything
that wasn’t wry, funny, or interesting, or all three. The last thing he said to
me was “Brad, this is serious”, delivered in that same familiar wry
Tom way. I didn’t want to believe it
then and I still can’t believe I’ll never
get to see my wonderful friend again.

I met Tom in I think late 1963, when we talked about me becoming his very first Ph.D. student. At the time he was an Acting Assistant Professor, and by University rules was not permitted to be a first reader on a dissertation. But it was blindingly obvious, even to a young graduate student, that Tom was launched on a stellar academic trajectory, and I had no doubt that he would be promoted to the requisite Assistant Professor position long before I needed a signature. And of course, so it was.

We worked together on establishing asymptotic properties of the nearest-neighbor pattern classification rule, and I always found Tom’s geometric intuition and mathematical insights beyond remarkable, they seemed super-human.

But I remember Tom’s human side, so to speak, even more than his mathematical side. He was a brilliant, generous, and supportive friend and advisor, with a dry wit that could momentarily create a pause in our conversation as his meaning dawned on me.

At an NSF PIs’ meeting in the early eighties,
the program director asked us to suggest models for communication over meteor-burst channels. Tom’s crack — “Consider an additive rock-noise channel model” — still brings a smile.

A giant has slipped away quietly and suddenly. Ever willing generously to engage, question and encourage, Tom was a brilliant lodestar for information theory, and his book with Joy Thomas is one reason why the field has attracted so many new adherents.
It is hard to have to believe that we will not
see his large smiling presence anymore.

Tom was one of my ten examiners in the qualifying exams this year, and undoubtedly the one I enjoyed the most. After I finished, he quipped “It seems your education has not gone waste!”. I resolved to get to know him better, but unfortunately that never happened.

My deepest condolences to his family, students and colleagues for their loss…

A deep and elegant thinker and a graceful gentleman – that’s the Tom Cover I had the privilege of knowing as a colleague and friend. Beyond physical boundaries, his intellectual legacy lives on. Thank you, Tom, for all the light you’ve brought to so many people.

This condolence is from the other side of Pacific Ocean. Although Late Professor Thomas M. Cover was not my thesis advisor, he was one of my examiners on the quals. At ISL of Stanford, I had an honor of learning a lot from several academic giants. Those wizards have their own characters. Tom was a mild gentleman with a deep insight. I still remember him playing at Stanford Golf Course singly and passing our novice foursome with a very polite greeting to us. Many people in Japan will miss him too.

Of course, what is on all of our minds is Tom. This is a tragic loss for all his friends and for a much wider circle of people who have benefited from his work. I was at his last seminar talk in Statistics and it was the best talk I have heard him give. At least I was able to tell him how much I enjoyed the talk and how much more interesting it was than other previous work on the St. Petersburg Paradox. That is the way I will remember him.
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I’m sorry to hear the news. It did get me thinking about Tom, though. I took three classes from him, and he was the chair of my thesis committee.

My first encounter with him was in the first lecture of Stat 200. To introduce maximum likelihood, he worked through the statistician’s approach to estimating the probability that the sun will rise tomorrow: treat the sun rising or not like independent coin flips with a biased coin, and estimate the probability p of that biased coin based on the number of observed sun rises so far. Quite different than the more model-based approach a physicist might adopt, but quite compelling.

Later I took information theory from him. It wasn’t that I was particularly eager to learn information theory, but I had learned that when you find a professor who teaches well you should make an effort to take everything that person teaches. As with the book that emerged from that class, his lectures were deep and clear. It was remarkable how much he could squeeze from a few first principle ideas, and how the class was structured to emphasize how those principles lead to a wealth of more specific results.

What I remember more, however, is the experience of going to his office. At first this was generally because I was stuck on a homework problem, and thought (silly me) that I might get some help with it. Inevitably, there were several of his PhD students already there talking about something. But I don’t think it was ever about the course. You’d knock on the door and Tom would boom out, “come in”. Then he’d smile at you like you were his long lost cousin and say “have a seat.” Usually this had to be on the floor because every other surface was covered with stacks of paper. And then he’d say something like: “We’re just thinking about Kolmogorov’s conjucuture that …., ” where the “that” was the last thing I actually understood in the sentence, “…and maybe you’ll be able to help us out.” Fat chance, but I would sit and listen and sometimes learn a little. I don’t think it ever helped me with the homework problem I was trying to solve, but it was pretty fun. I started dropping by even when I didn’t have a homework problem I needed help with.

One time, though, he rummaged amongst a bunch a paper and pulled out a poster of the CIE chromaticity diagram made by PhotoResearch. It was one of the colored ones, where each part of the diagram was designed to convey what stimuli of that chromaticity would look like. So he says, “You know about color, why is the center of this diagram white?” Well, this was finally my chance to say something I understood, so I start in about cones and color matching functions and how chromaticity is computed and why the center is the chromaticity of an equal energy white and the fact that …. Tom nods for a while but I get the sense I’m not really answering his question. Suddenly he gets all excited and says “Yes yes yes I get it. It’s the same reason that you can see through water.” To this day I have no idea what he meant, but I’m sure it was deep, and I thought I’d better quit while I was ahead. So I said “Exactly!” and we all turned our attention back to information theory.

Beyond what I learned from him (and the info theory has stayed with me and indeed showed up in various papers I’ve written), he was always kind to me. When I finished my thesis, he made the effort to take me lunch at the faculty club and spend an hour chit chatting and wishing me well in my career, and I’ve always appreciated that.

I am so much saddened to hear this sudden news. I have very fond memories of Professor Cover during my first weeks and months at Stanford. I was just talking about him fondly yesterday with a colleague of mine here at ICASSP in Kyoto. What a kind and caring individual he was, apart from being a giant in his field and passionate about his work. His memory will live on through his work and his many outstanding students.
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I am extremely saddened to have learned about Tom’s passing. I spoke to him last at the recent ISIT in St. Petersburg last August. Anne-marie and I had quite a bit of interaction with Tom and Karen during this symposium. At one occasion, Tom mentioned to me how lucky we have been to have witnessed and been part of the development of multi-user information theory. He added how fortunate young people, who now enter the area, are: “the field is a goldmine for research for at least another 30 years”.
I first met Tom at the Noordwijk ISIT in 1970, where we both presented a paper on multi-user channels. A warm and collegial friendship developed between us since then.
We saw each other at many conferences around the world and I could visit Stanford several times under Tom’s auspices.
Tom was an outstanding and charismatic speaker. I vividly remember his acceptance speech when receiving the Best Paper Award for his paper “Broadcast Channels” (1972) and his Shannon Lecture at the ISIT in San Diego (1990).
I admire Tom and thank him for the association I could have with him over a period of 40 years.

I am sad to hear the passing away of Prof. Tom Cover, a great information theorist and a kind and caring mentor. I was at Stanford in 1972 and enjoyed having conversations with him and remembered his notes using the famous yellow pad. He can be humourous at times but is really concerned about quality in research. His papers are deep and today I am still doing research based on his two important papers in universal portfolios published in 1991 and 1996. In my last e-mail communication with him a few years ago, he replied with the words, “we are growing old”. I don’t really understand what it means at that time but now probably I do. It is a great loss to the infomation theory community with the passing away of a giant.

It was a real privilege for me to be one of Tom Cover’s Ph.D. students. Tom was brilliant, funny, humble, and extraordinarily supportive and generous with his time. Others have written more eloquently than I could about Tom’s insight and character, so I’ll just include a few quirky stories that illustrate the fun that we students had in Tom’s research group.

Some of Tom’s former students might remember his proof that all games between evenly matched opponents in any sport whatsoever are equally exciting. (There was a little handwaving to deal with discontinuities in the score, but I think the basic idea was that one can focus on the continuously evolving probability that the home team will win and thereby turn all games — suitably normalized — into essentially equivalent random walks.)

It may have been an application of probability and statistics to sports that led us in one research group meeting to go off on a tangent about extreme sports waiting to be invented. Tom imagined something like a 10-meter platform dive onto concrete. Bringing information theory into the picture, he stipulated that the athlete would have to answer one binary question after landing.

One of Tom’s least successful explanations of statistical principles was given to a police officer who pulled him over for exceeding the ridiculously low speed limit of 25 mph on Embarcadero or Middlefield Rd. When the officer learned that Tom lived nearby, he sought to impress upon Tom the need for special caution when driving near home, saying something like “50 percent of all accidents occur within 3 miles of the home.” Somewhat exasperated, Tom shot back, “That’s because 50 percent of all DRIVING takes place within 3 miles of the home.” As it turned out, that wasn’t the best response.

Even if Tom wasn’t in the middle of the action, his playful approach to problem-solving rubbed off on his grad students. One time when Andrew Nobel, Mitch Trott, and I were in our office, one of us had to make a phone call but didn’t have the phone number handy. One of the other two office mates — Andrew, I think — asked, “Why don’t you just rederive it from first principles?”

While we were still in the Durand Building, ISL professors were asked for input regarding the design of a new building that was being considered. Tom quickly put together a tongue-in-cheek proposal that involved (among other things) a river that would flow throughout the building and allow faculty members to float memos downstream to the dean.

Rest in peace, Tom. I miss your wit and warmth, but I hope that someday we’ll meet again and I’ll have a chance to see what progress you’ve made in multi-user information theory.

I first met Tom in 1960 when I joined his MIT fraternity. He used to play poker all evening with John Sununu and others. Most of the other players usually flunked out while these two continued to play ever night at the fraternity house. Even as an undergrad Tom was always full of ideas which he expressed with his unique childlike excitement. I decided to go to Stanford for my graduate work partly because of Tom who later served on my Ph.D committee. Tom was one of the most creative thinkers in our field of Information Theory.

What a loss to all of us…to science…and to information theory community! He was a remarkable man we all aspire to be like when it comes to research, inspiring teaching, and sense of humour. He defied aging of the grey cells to the last days of his life! He was extremely sharp…I remember talking to him during the Houston Globecom in Dec. 2011 (just 4 months ago) after he gave a motivating talk with an overfilled room as usual! Given his marks on all of us and science, he will be always alive with us…and with all those who love science!

Tom was the main reason I accepted this job in EE. When he interviewed me, only a short year ago, he didn’t talk about my qualifications for the job, what had brought me to interview for EE or anything job related. We sat in his office talking about baseball, a sport that we talked about daily in my time as his faculty administrator. He loved the Giants, I am a lifelong Cubs fan and yet we still had plenty to talk about. We cheered on the Stanford Football team together and we discussed the physics of shot put and discus, he was fascinated by how it all worked and came to me as his ‘resident expert’. He was a brilliant and funny man, and he will be greatly missed here

I can’t think of Tom gone. He stayed young and playful at all times, even when dealing with the most difficult dilemmas – in science or life.. When I came to Stanford and became his PhD students, I felt I made the right choice, but only later I realized how lucky I was. Knowing him was an unusual privilege, honor, inspiration, and most of all fun. Although I did not continue with IT, Tom was my ultimate role model – as the greatest, yet the most humble, person, scientist, and friend. We miss you!!!

When I think of Prof. Cover, I recall his easy-going, humble, gentle manner, his fantastic sense of humor, his love of all kinds of interesting problems, and, of course, his brilliance. Two stories, in particular, come to mind.

Others have commented on Prof. Cover’s athleticism, and some may remember that he allegedly played on the ISL softball team at some point. I say “allegedly” because during my years in ISL from 1991-1996, I never actually saw Prof. Cover play. Oh, he would sign up to play, but at game time he was always missing in action. One year I saw Prof. Cover in Durand a few weeks before softball season was starting, and I said, “Hi, Prof. Cover. Are you going to play softball this year, or are you just going to sign up?” He responded by bursting out laughing and walking away (still laughing). For about a year after that, every time I saw him, Prof. Cover would start laughing, pointing, and muttering something about “just signing up.” (I will note, however, that he still did not actually play….)

I also fondly recall my quals session with Prof. Cover. He was my last professor, and my brain and attitude were both waning by the time I got to his office. Knowing how smart Prof. Cover was and how difficult many information theory topics can be for me, the exam had the potential to be an absolute nightmare. I think Prof. Cover was also tired of the quals, though, because as soon as I sat down, he said, “I want to talk about duality. Can you give me some examples of duals?” He had no patience for the “safe” answers; he wanted “good and evil,” “sweet and sour,” and any other crazy duals I could imagine. That exam was (dare I say it?) fun and a welcome finish to my quals exam. I remember walking out of the exam and thinking that I liked Prof. Cover even more than I previously had because his quals exam was completely out of the box. Of course, what else would it be?

Prof. Cover brought a special energy and a unique point of view to the world, and I am so glad to have benefitted from his generosity in sharing both. Rest in peace, Prof. Cover.

I was shocked to hear of Tom’s passing.
I benefited from only a couple of conversations with him, but they were unforgettable experiences, ranging from
the information density of black holes to hand-drawn, cartoon versions of Lena. It is sad for me to think that there will not be a third conversation, and that for the next generation of students, there will not even be a first.

The outpouring of love for Tom Cover and the sadness expressed over his death are a testament to how fully he inhabited this life. He wasn’t JUST a brilliant philosopher and devotee of physics, he wasn’t JUST a sports fanatic, he wasn’t JUST an artful investor, he wasn’t JUST a consummate puzzler, he wasn’t JUST a Deadhead, he wasn’t JUST a meticulous editor, he wasn’t JUST a natural athlete, he wasn’t JUST a trickster, he wasn’t JUST an extremely generous human being, he wasn’t JUST the most gracious host you would ever meet, and he wasn’t JUST the life of the party. He figured out how to do it all – clever man!

He was always on the lookout for the next good laugh, and I will always think of him leaning back in a chair grinning at the ceiling as he absorbed the latest bit of irony.

Tom was a rare individual. His way of doing things was just different. Including the process of “producing research.”

Tom was one of those people that on their daily commute to work (which was quite short in Tom’s case), would dream up at least 10 new fun problems/puzzles. With tremendous enthusiasm, Tom would then share the best of the bunch with his students, or anyone else that just happened to be there for one of his numerous smoking (errr… brainstorming) breaks, outside his huge corner office in Durand. Having been carefully screened (and smoked out), the real gems were then brought to the ultimate stage: the Wednesday research group meetings.

Many ideas were abandoned and never resurfaced; others led to false starts; some made it into Tom’s teachings; some morphed into homework problems in his book; but almost all resulted in just plain old good fun.

Though I didn’t have the pleasure and privilege of meeting Tom until I started work in the EE Department in 2009, I always enjoyed our occasional discussions. Tom was always engaging, thoughtful, and caring. He paid attention to people and departmental dynamics, and wanted the best for everyone. Though I haven’t seen him since I left the department in 2011, I’m very sorry to hear of our loss.

In 1999 I had the privilege to spend my sabbatical with Tom in Stanford. This was a semester of joy, fun, and intellectual happiness. We talked, we joked, we ate, and we had a lot of fun. Every time I’ve met Tom since then I learned something new: sometimes a new jewel in information theory, sometimes just a funny fact of life or politics. It was never boring talking to Tom. We miss him so much.

I haven’t had any contact with Tom since I left Stanford in 1993, but I’ve thought of him often. Many of my best memories of that time are of hanging out with Tom and his research group just tossing around ideas that ranged from off-the-wall to brilliant. What a loss.

Our son Jim was blessed to have Tom as his advisor, and when Jim got his MS he wanted us to meet Tom. We appeaered in Tom’s office one Sat. morning and Tom jumped to his feet to greet us. He scooted around clearing papers from every horizontal surface so we could all sit down. He was one of the most delightful people we have ever met and we knew of his outstanding knowledge from Jim’s and other grad student’s comments about him. Though he was a recognized world expert in Information Theory, he was so humble and thoughtful of his students.
We too will miss him through the memories of our meetings with him and through the wonderful experiences Jim and his other students had with him.
Rest in peace Tom. We’ll meet again.
John and Mary Roche

I first met Tom when I came to Stanford in Fall 2010. Since then Tom went on to become my co-advisor and I had the honor of studying information theory from him.

Words really are not enough to express what Tom was to information theory, to Stanford, and his students. Being his student for more than a year has given me memories that will last a lifetime.

Tom, I’ll miss that all-knowing sparkle in your eyes, that uncanny ability to distill ideas into simple words and diagrams, and that unusual combination of charisma and humility that made you the best teacher I have had.

I remember one of the comments a student wrote for Tom in his EE376A (information theory) course – “Tom Cover is the Jack Nicholson of Information Theory”

In the first week of March 2012, after our usual Wednesday research seminar, as we were wrapping up – I told Tom about a recent proof I read and would like to tell him about in the next meeting. He smiled and said “You bet !”. Alas, there was no next meeting.

Tom, you taught me Information theory, how to play a tennis backhand, and so much more. I envy those who got to spend more time with you, and feel sorry for those who will never get the chance to meet you. Rest in Peace

I am deeply grieved at Tom’s passing. He was a good friend and we spent many hours discussing application of complexity to biological information processing. I loved his playful wry sense of humor. Perhaps something no one else can say is that, I was the first woman to ever take his information theory class and invited him to Lagunita women’s dorm in 1967, where I was an RA. He wanted to meet women and I was happy to oblige. He roared in his Mustang (remember Marty?) from Lake Tahoe where he had just won the black jack– as student grapevine story went, he was barred from many casinos from playing as he had worked out the winning strategy. Rest in peace Tom, you will be in our hearts for ever. We were blessed to know you and learn from you. Our condolences to your family.

The untimely passing of Tom Cover has shaken me to a degree that transcends anything I anticipated. Too many wonderful persons who loved and sculpted the subject of information theory have left us recently, but for me the loss of Tom is more devastating in ways some of which I understand and others of which are beyond my comprehension.

There is no need for me to recount his contributions and his brilliance, since many of those who have have contributed their sentiments above have done that quite thoroughly. Let it suffice to say that Tom was both literally and figuratively a GIANT among us – as a colleague, an adviser, a teacher, a researcher, a role model, an athlete, an entertainer, a warm spirit and a font of creativity.

Tom was my tennis partner is locales all around the Northern Hemisphere. Tom and Karen were my dear companions at restaurants and nightspots on several continents. The memories of those special occasions have been repeatedly sweeping into my mind over the last two weeks. On Tuesday, February 7, Tom and Karen and I dined together in the bar and grill of the Catamaran Resort during ITA 2012 in San Diego. Everything seemed the same as always, especially that glint in Tom’s eyes whenever (and, as always, it was often) he made a witty and/or intriguing comment.

Tom, I miss you irreplaceably in a way that far surpasses my ability to translate into words. Karen, my deepest condolences and heartfelt sympathy. Toby

I had the privilege of being Tom’s PhD student at Stanford. Outside my family, he is certainly the person that influenced me the most. And given that we never collaborated directly, I still have no idea how he did it. In fact, I only really realized how deep and permanent his influence had been after leaving Stanford. My only consolation is that (to his annoyance) I got a chance to tell him all this face-to-face a few years ago.

Tom was the most sophisticated thinker I have ever known, and the person with the coolest, most ironic and most surprising sense of humor. He was fair, honest and a really kind man. Seeing him at a meeting was always the highlight of the conference for me. His passing is really really sad. I wasn’t ready — and I don’t think I would have ever been.

A huge majority of comments come from those who knew Tom as a professor and a contributor to the field of Information Theory. I first new him the summer before I entered MIT in 1958, and then as a fraternity brother for the next two years. The amazing thing is that many of the comments about his character and personality in his adult years are not much different from the young man I knew! He loved life, and was an encouragement to many of us as we began our studies at MIT.

I am speechless. I graduated with my PhD in Electrical Engineering from Stanford last quarter. I unsubscribed from all emailing lists which is why I didn’t learn about this until now.

What can I say? One of the most momentous moments in my PhD career was not only to take Tom Cover classes, which I greatly enjoyed, but a meeting that I had with him after I had a horrible results for the midterm exam of EE376A (I don’t want to make excuses but it was my first year as graduate student having spent 7 years outside academia). Tom’s encouragement and kind words made me study harder and not only I eventually did very well in the final but I also decided to take his second class, EE376B which happened to be offered that year. And BTW, I also had him in my quals committee .

The world of engineering and science has lost one of its giants. He was a great scientists but also, based on the brief interactions I had with him 1-1, a great human being. Rest In Pace Tom Cover.

I met Tom in fall 2010, Meeting different from conventional meetings…
I was Tom’s student, but a different student…
I’ve never been at Stanford University and never saw him but I was his student through the web and participate in his classroom. He was an inspiring professor and perfect model.
At this time I think “Entropy of Tom” is infinite…
and the proof is so simple…
Although I never saw him but I will miss him…
Tom will be continued… forever…

When I first arrived at Stanford as a naive undergrad, I had little idea what I wanted to study. Math, economics and even philosophy all seemed quite tempting. On one typically sunny day, I went to browse in the Stanford bookstore. There, sitting on the shelf was a book that forced me to pick it up. It had a purple cover with a greenish Mandelbrot set, emblazoned with those magical words “Information Theory.” It was the newly published book by Cover and Thomas.

The words and ideas in the book so intrigued me that I soon found myself asking others what major I would have to declare in order to study this mystical subject called information theory. That, in short, is how I went on to study electrical engineering.

There were many great classes at Stanford, but I always looked forward to attending Tom’s information theory class with a special sense of anticipation. To me, the class was the ultimate combination of the coolest subject and the coolest lecturer. When those sparkling ideas of Shannon came out with Tom’s mesmerizing cadences, sprinkled with those wry witticisms and startling insights which boggled an undergraduate’s mind, it was a true intellectual feast.

A few years ago, on a visit to Stanford, I finally had the chance to tell Tom about how I became an EE major and a member of the IT community. Tom paused briefly, shook my hand warmly, with that all-too-familiar sparkle in his eye.

I am so terribly saddened to learn of Tom’s departure. Tom was not just brilliant and creative but a fun and stimulating presence. I marveled at his ability to follow esoteric thoughts, investigate intractable ideas, explore hard problems, and come down on his feet with simply beautiful solutions, all of it while having fun. I have found later in my professional life that his brilliance, his intuition, his playfulness, his generosity were very unique. Since I left his group in 1971, I have missed Tom and the stimulating environment he created. What a chance it was to know you, Tom! Thank you for ever.

Like so many others I remember Tom for many things, but mainly for our interaction in a course on Information Theory at Stanford. Like the others I learned a lot about information theory from Tom, but unlike anyone else I was the teacher in that IT course in 1960 and Tom was, in theory, a student. By the end of the first class I had asked Tom to serve as grader for the weekly problem sets assigned the students.

Imagine, if you can, starting to teach a new class in information theory at Stanford in
those days with Tom Cover grading your weekly class assignments. I had many
opportunities to interact with Tom since then but whatever we talked about when we met I know we both thought back to that special class in information theory and our weekly meetings over fifty years ago.

I was a new PhD student in Statistics at Stanford in 1964 and soon met Tom. He came around often to Sequoia Hall to hang out with his friends who were finishing their dissertations. He was brilliant, personable, and fun to listen to, and has often been in my thoughts. So sad to discover that he is gone.

When I met Tom in 1975 he was young and single, the epitome of the cool professor. He drove an exotic but erratic Lotus Europa. He had a beard. He smoked cigars. And what a grin he had to go with his bon mots!

At Ph.D. qualifying exams, Tom had the most eclectic questions, making it positively fun. He was my number one choice for Ph.D. advisor; there was no number two. I have never met Tom’s equal in his ability to create and share that rare mixture of intense intellectual challenge and playfulness.

Tom’s life was very well lived: multi-dimensional and not at all a typical sequence.

Before I came to Stanford, in 1980, Jack Koplowitz ,who was visiting the Technion, told me about a genius of Information Theory I am going to meet at ISL: Tom Cover. Of course, Tom Cover exceeded all expectations!
His courses on Information Theory (that became the famous textbook later!) and his
course on Pattern Recognition were
wonderfully different and mesmerizing.
Although I did my thesis with another
great Tom at ISL (Tom Kailath) I was lucky
enough to have collaborated with Tom Cover on one paper, on linear separability, following his Pattern Recognition course.
I am so grateful for having had the chance to
spend many long hours with Tom Cover, discussing our paper, and life in general.
Since the Stanford years, meeting him in many places over the world was always a great pleasure. He was always enthusiastic and had interesting puzzles and challenges to address. I am so sorry he left us: he was
a true giant, and a most generous and kind person. May his memory be always blessed!

A few years ago I had a number of long telephone conversations with Tom. We discussed his ideas on the Universal Portfolio and finance and even explored some possible extensions to the idea over the phone. We talked about the whole history of the idea and as we did we very naturally came around to talk about poker. The he really perked up.

Tom described how as a student he would play poker in one of the California “card rooms”. He had developed what he described as an optimal approach to playing some specific poker variation. He had worked out all the probabilities of play. When he applied the method, he so strongly dominated his competition that everyone simply stopped playing against him. He took this as a real set back but in his fashion he thought through the problem, moved to a different card room in a nearby town and started again, but this time he deliberately played sub-optimally. He found that gauging his level of play so that the other player’s didn’t perceive him as dominate, but rather just a little lucky on that given day worked to keep them playing against him hour after hour, day after day, and week after week.

He told the story with such delight and good natured giddiness that neither of us could stop laughing. Someone listening in might have thought we had know each other for years rather than just a few hours over the phone.

I didn’t know Tom to nearly the extent that all of those who have contributed to this memoriam did, but in those moments, I think I did get a glimpse of all that endeared him to all of you.

What I will always remember of Tom is his laughter, especially as a tangible manifestation of his delight in the elegance of mathematical results. His stature as an Information Theorist, his wonderful personality, and his eagerness to interact with students allowed him to create what would be better described as a school, in the sense of the ancient Greek philosophers, rather than a group.
Studying with him at Stanford was the most stimulating and exhilarating period of my career, and I will always be grateful to Tom for offering me this opportunity.

Tom was always very generous. He treated me many times to lunches at the Faculty Club where there was great food and great conversation about stocks, sports, puzzles and other topics of the day. I’ll really miss him.

Today I was utterly shocked to hear of Tom’s passing. We were engaged in the early 1960′s, but parted soon after he completed his Ph.D. In the years following I completed my college education and taught high school English and some community college writing classes for the next 28 years. I loved him and his entire family. His parents wrote to me every Christmas until both of them died. It is wonderful to read the tributes to him and to realize the positive effect he had on so many lives. I mourn his loss with his family, brothers, and friends.

At Tresidder Union in 1967, I had a chance dining table encounter a very intelligent and intense young man. He was extraordinarily engaging, and it turned out he, too, was interested in this rather new field, “information theory” – on the faculty, in fact – Tom Cover, his name. After this stroke of good luck, eventually Tom became my Ph.D. thesis supervisor, for which I will always be grateful.
His curiosity was endless, as was his fascination with paths of reasoning that others might never notice, let alone have the inclination and courage to follow. He invited his listener into the depths of mathematical deduction by starting with a seductively simple example, laid out with unassuming clarity. Tom taught me an aesthetic in research, a sensibility and good taste in a result, and what it meant to frame a problem with brilliant panache. I will always revere his gentle humor and unique insights as he explored strange statistical worlds. On the occasion of his 60th birthday he made a point of telling me that he was not retiring: Let not the birthday celebration create any such confusion. For him, to retire was “to be out of the game.”
Having changed how the world thinks about games, Tom will never be out of the game. I have been blessed to have spent my moments in the game with a such a special genius.

I have read with gratitude, and a very sad pleasure, the many heartfelt testaments from Tom’s students and colleaques.
I also attended Stanford, but studiously avoided any upper divison science or math classes. This in no way diminished the great man crush I had for him for over 30 years. Denise,(# 86) you have captured beautifully the Tom many of us knew and loved, I will also carry with me that image of Tom’s grin and the brilliant sparkle in his eyes.

I met Tom about ten years ago when I was invited to play golf by another friend. Almost every Monday we would play golf at Coyote Creek Golf club in Morgan Hill. Our format was a Skins Game if we had more that four playing or a Nassau match game if we had only four playing. Sometimes we would play a strange game called Oink if we only had three players. I always enjoyed it when Tom played. He always kept track of the scores, putts, birdies, etc. Afterward we would go to the 19th hole and discuss golf plus numerous other matters, including politics, the economy, and the stock market. Tom always had a unique take on these matters.
Every week we all remember Tom’s life on Monday’s with us. He is sorely missed.

Tom was incredibly kind to all junior members of the Society. It was he who encouraged me to run for BoG. He of course was incredibly funny. I remember his listening to some boring description I was giving of some protocol and all of sudden he said “ACK, ACK, ACK – makes me think of Mars Attacks!” He is very sorely missed.

I first saw Tom when I sat in on his information theory class, where his philosophical and conceptual approach made the subject sing.
He became a reader on my thesis. When I first told him about the major theorem of my thesis, he said he thought the result was wrong and said he thought he could find a counter example. I left his office in shock, and had little sleep for the next few nights. I wondered what error I could have made, but couldn’t find my mistake. Finally I met with him again and he said the result was correct – perhaps the happiest day of my time at Stanford.

We later became poker buddies, played as partners at backgammon tournaments, worked on investment theory, and discussed diverse mathematical problems, often meeting at Joannie’s café on California Avenue. What fun we had.

I never knew Tom on campus. I never understood what he did – he was smart, but I had no idea of how absolutely brilliant he was.
I knew him from dropping in to his & Karin’s house. Door always open, smile always genuine, hug – like a big teddy bear and balanced off with amazing kindness and generosity. Tom’s inner grace extened in so any directions with the same genuine emotions. Txs, Tom -I haven’t a clue about game theory or poker but, I treasure the memories and you left your mark as a role model, my good fortune to have known you.

I was looking for Tom Cover’s web page today to look for his new papers on Info. theory’s applications to sports and stock trading, and ran into this sad news. I took a UG course on Info. Theory in Spring 2000, which was to introduce me to his “classic” text — Elements of Information Theory. The simplicity of the book was misleading; it took an incredible amount of effort and concentration to get even a reasonable import of the simple text, equations and the smooth exposition in those chapters. The course was on information theory and Tom’s book was absolutely riveting and fascinating. It soon impressed upon me the fact that the Information theory is the unifying theory between statistical signal processing and pattern recognition (which is also fashionably called as machine learning). Data compression, coding for the communications in noisy channels are the underlying problems in pattern recognition too, except that in this case we don’t have the signal generator in our hand — it’s a naturally occurring signal like speech, image, video, stock price, a game score etc, which has been coded up through nature’s code book and relayed over nature’s multimodal noisy channel.
Even though, I have been just a distant reader of his book, and never have interacted with him, the influence that he had on my research and living is incredible. Thank you very much Prof. Tom Cover.

I never knew Tom. I never went to Stanford. I “was” not an Information Theorist. I stumbled upon this site because a friend of mine mentioned that a great scientist called Tom had passed. After reading all the testimonials above, I got a lump in my throat. I feel I know him already, regret never knowing him, and regret even more his passing. You all whose lives he touched should count yourself lucky and keep him alive in you and pass on the “Tom” in you…

Adieu…

PS: Information Theory has just got a new convert. Anybosy who has any “101″ basic info to get me started should please send to my mailbox at masterchike@yahoo.com